An implant for implantation in a lumen includes a plurality of struts, with intervening openings therebetween. The implant also includes narrow connecting pieces, bridging at least some of the openings so as to interconnect the struts. Exertion of a first outward radial force on the struts causes the implant to open to a first diameter by opening the intervening openings between the struts. The narrow connecting pieces are adapted to break under exertion on the struts of a second outward radial force, greater than the first outward radial force, so that the implant opens to a second diameter, greater than the first diameter.
